The 2001FP is a great display, especially for the money. The Mac Mini seems to run it just fine despite the under-powered 32 MB GPU. The only time I've found my Mac Mini to really slow down was when playing around with iMovie adding special effects. I don't use iMovie often, as I said, no MiniDV to be importing and editting - I just wanted to try it out. I also don't try to run any intensive games on my Mini. For any and all daily tasks (email/browsing/iTunes/iCal/IM/etc) and some moderate image editing the Mac Mini and 2001FP work great.
Expose and Dashboard would probably fly in and out more smoothly on a more powerful machine but I don't find it to be choppy or too sluggish on my Mini. The only strong recommendation I would make for the Mini is to be sure to get 1 GB of RAM - 512 MB minimum. Also, it's much cheaper to do the 1 GB yourself.